Question

What is the wavelength of a photon emitted during a transition from $n=5$ state to $n=2$ state in the hydrogen atom?

• A. $434nm$
• B. $450nm$
• C. $350nm$
• D. $525nm$

Answer 1

Answer: (A)

$434nm$

$\frac{1}{\lambda }=R[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$

$\frac{1}{\lambda }=109677.6c{m}^{-1}\times [\frac{1}{2^2}-\frac{1}{5^2}]$

$\frac{1}{\lambda }=23032.3c{m}^{-1}$

$\lambda =4.34\times {10}^{-5}cm$

Convert unit from cm to nm

1 cm $={10}^{7}nm$

$\lambda =4.34\times {10}^{-5}cm\times \frac{{10}^{7}nm}{1cm}$

$\lambda =434nm$